In 2-dimensional geometric constraint solving, graph-based techniques are a dominant approach, particularly in CAD context. These methods transform the geometric problem into a graph which is decomposed into small sub-graphs. Each one is solved, separately, and the final solution is obtained by recomposing the solved sub-graphs. To the best of our knowledge, there is no random geometric constraint graph generator so far. In this paper, we introduce a simple, but efficient generator that produces any possible geometric configuration. It would be parameterized to generate graphs with some desirable proprieties, like highly or weakly decomposable graphs, or restricting the generated graph to a specific class of geometric configuration. Generated graphs can be used as a benchmark to make consistent tests, or to observe algorithm behaviour on the geometric constraint graphs with different sizes and structural properties. We prove that our generator is complete and suitable for two main classes of solving approaches.

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Abstract. Gastroscopy is a common procedure for diagnosing the diseases in upper GI tract, in which a large number of localized and sometimes unstructured images on different parts of the upper GI tract are captured. While it is effective, the procedure also requires experienced doctors to carefully exam these images in real time. As a result, errors may occur causing miss and/or false diagnosis. This paper presents a holographic displaying system that can display the images in a 3D structured manner. It consists of four steps. First, the gastroscopy images are acquired from the standard gastroscopy procedure. Second, a 3D image is generated by means of panoramic mapping. Third, the 3D image is transferred into four images. Finally, the images are displayed in a 4-side pseudo 3D holographic system. The new system is capable of showing 3D structured view, based on which the doctor can carry on diagnosis more effectively. With further development, it is expected that the new system will find practical applications in hospital soon.